Yes! You can reuse your old Ubuntu Mate 16.04 installation from a Raspberry Pi 3 with a new B+.
Trying to boot the B+ with the old SD without modifications, will result in the rainbow screen with thunderbolt screen showing up.
-
From your old Rpi, update the firmware(kernel.img&co) on the boot partition running
sudo rpi-update
. This will be enough to boot on the B+ but the wireless card will still not work. -
Set a country code for the wireless adapter in your wpa-supplicant.conf (usually under /etc/wpa-supplicant/) adding
country=GB
. -
Get all the files contained in
https://github.com/RPi-Distro/firmware-nonfree/tree/master/brcm
and copy them over the content in/lib/firmware/brcm
. This will add a few new and updated drivers for the B+ wireless adapter.